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The gravitational microlensing method of discovering exoplanets and multi-star systems can produce degenerate solutions, some of which require in-depth analysis to uncover. We propose a new parameter space that can be used to sample potential solutions more efficiently and is more robust at finding all degenerate solutions. We identified two new parameters, k and h, that can be sampled in place of the mass ratios and separations of the systems under analysis to identify degenerate solutions. The parameter k is related to the size of the central caustic, \\(\\Delta\\xi_c\\), while h is related to the distance of a point along the k contour from log(s)=0, where s is the projected planet-host separation. In this work, we present the characteristics of these parameters and the tests we conducted to prove their efficacy.

We measure the Einstein radius of the single-lens microlensing event KMT-2022-BLG-2397 to be theta_E=24.8 +- 3.6 uas, placing it at the upper shore of the Einstein Desert, 9 < theta_E / uas < 25, between free-floating planets (FFPs) and bulge brown dwarfs (BDs). In contrast to the six BD (25 < theta_E < 50) events presented by Gould+22, which all had giant-star source stars, KMT-2022-BLG-2397 has a dwarf-star source, with angular radius theta_* ~ 0.9 uas. This prompts us to study the relative utility of dwarf and giant sources for characterizing FFPs and BDs from finite-source point-lens (FSPL) microlensing events. We find `dwarfs' (including main-sequence stars and subgiants) are likely to yield twice as many theta_E measurements for BDs and a comparable (but more difficult to quantify) improvement for FFPs. We show that neither current nor planned experiments will yield complete mass measurements of isolated bulge BDs, nor will any other planned experiment yield as many theta_E measurements for these objects as KMT. Thus, the currently anticipated 10-year KMT survey will remain the best way to study bulge BDs for several decades to come.

Chang-Refsdal (C-R) lensing, which refers to the gravitational lensing of a point mass perturbed by a constant external shear, provides a good approximation in describing lensing behaviors of either a very wide or a very close binary lens. C-R lensing events, which are identified by short-term anomalies near the peak of a high-magnification lensing light curves, are routinely detected from lensing surveys, but not much attention is paid to them. In this paper, we point out that C-R lensing events provide an important channel to detect planets in binaries, both in close and wide binary systems. Detecting planets through the C-R lensing event channel is possible because the planet-induced perturbation occurs in the same region of the C-R lensing-induced anomaly and thus the existence of the planet can be identified by the additional deviation in the central perturbation. By presenting the analysis of the actually observed C-R lensing event OGLE-2015-BLG-1319, we demonstrate that dense and high-precision coverage of a C-R lensing-induced perturbation can provide a strong constraint on the existence of a planet in the wide range of the planet parameters. The sample of an increased number of microlensing planets in binary systems will provide important observational constraints in giving shape to the details of the planet formation scenario which has been restricted to the case of single stars.

We inspect 4 microlensing events KMT-2021-BLG-1968, KMT-2021-BLG-2010, KMT-2022-BLG-0371, and KMT-2022-BLG-1013, for which the light curves exhibit partially covered short-term central anomalies. We conduct detailed analyses of the events with the aim of revealing the nature of the anomalies. We test various models that can give rise to the anomalies of the individual events including the binary-lens (2L1S) and binary-source (1L2S) interpretations. Under the 2L1S interpretation, we thoroughly inspect the parameter space to check the existence of degenerate solutions, and if they exist, we test the feasibility of resolving the degeneracy. We find that the anomalies in KMT-2021-BLG-2010 and KMT-2022-BLG-1013 are uniquely defined by planetary-lens interpretations with the planet-to-host mass ratios of \\(q\\sim 2.8\\times 10^{-3}\\) and \\(\\sim 1.6\\times 10^{-3}\\), respectively. For KMT-2022-BLG-0371, a planetary solution with a mass ratio \\(q\\sim 4\\times 10^{-4}\\) is strongly favored over the other three degenerate 2L1S solutions with different mass ratios based on the \\(\\chi^2\\) and relative proper motion arguments, and a 1L2S solution is clearly ruled out. For KMT-2021-BLG-1968, on the other hand, we find that the anomaly can be explained either by a planetary or a binary-source interpretation, making it difficult to firmly identify the nature of the anomaly. From the Bayesian analyses of the identified planetary events, we estimate that the masses of the planet and host are \\((M_{\\rm p}/M_{\\rm J}, M_{\\rm h}/M_\\odot) = (1.07^{+1.15}_{-0.68}, 0.37^{+0.40}_{-0.23})\\), \\((0.26^{+0.13}_{-0.11}, 0.63^{+0.32}_{-0.28})\\), and \\((0.31^{+0.46}_{-0.16}, 0.18^{+0.28}_{-0.10})\\) for KMT-2021-BLG-2010L, KMT-2022-BLG-0371L, and KMT-2022-BLG-1013L, respectively.

We investigate the microlensing data collected during the 2017--2019 seasons in the peripheral Galactic bulge fields with the aim of finding planetary signals in microlensing light curves observed with relatively sparse coverage. We first sort out lensing events with weak short-term anomalies in the lensing light curves from the visual inspection of all non-prime-field events, and then test various interpretations of the anomalies. From this procedure, we find two previously unidentified candidate planetary lensing events KMT-2017-BLG-0673 and KMT-2019-BLG-0414. It is found that the planetary signal of KMT-2017-BLG-0673 was produced by the source crossing over a planet-induced caustic, but it was previously missed because of the sparse coverage of the signal. On the other hand, the possibly planetary signal of KMT-2019-BLG-0414 was generated without caustic crossing, and it was previously missed due to the weakness of the signal. We identify a unique planetary solution for KMT-2017-BLG-0673. However, for KMT-2019-BLG-0414, we identify two pairs of planetary solutions, for each of which there are two solutions caused by the close-wide degeneracy, and a slightly less favored binary-source solution, in which a single lens mass gravitationally magnified a rapidly orbiting binary source with a faint companion (xallarap). From Bayesian analyses, it is estimated that the planet KMT-2017-BLG-0673Lb has a mass of \\(3.7^{+2.2}_{-2.1}~M_{\\rm J}\\), and it is orbiting a late K-type host star with a mass of \\(0.63^{+0.37}_{-0.35}~M_\\odot\\). Under the planetary interpretation of KMT-2010-BLG-0414L, a star with a mass of \\(0.74^{+0.43}_{-0.38}~M_\\odot\\) hosts a planet with a mass of \\(\\sim 3.2\\)--3.6~\\(M_{\\rm J}\\) depending on the solution. We discuss the possible resolution of the planet-xallarap degeneracy of KMT-2019-BLG-0414 by future adaptive-optics observations on 30~m class telescopes.

We systematically inspect the microlensing data acquired by the KMTNet survey during the previous seasons in order to find anomalous lensing events for which the anomalies in the lensing light curves cannot be explained by the usual binary-lens or binary-source interpretations. From the inspection, we find that interpreting the three lensing events OGLE-2018-BLG-0584, KMT-2018-BLG-2119, and KMT-2021-BLG-1122 requires four-body (lens+source) models, in which either both the lens and source are binaries (2L2S event) or the lens is a triple system (3L1S event). Following the analyses of the 2L2S events presented in \\citet{Han2023}, here we present the 3L1S analysis of the KMT-2021-BLG-1122. It is found that the lens of the event KMT-2021-BLG-1122 is composed of three masses, in which the projected separations (normalized to the angular Einstein radius) and mass ratios between the lens companions and the primary are \\((s_2, q_2)\\sim (1.4, 0.53)\\) and \\((s_3, q_3) \\sim (1.6, 0.24)\\). By conducting a Bayesian analysis, we estimate that the masses of the individual lens components are \\((M_1, M_2, M_3)\\sim (0.47\\,M_\\odot, 0.24\\,M_\\odot, 0.11\\,M_\\odot)\\). The companions are separated in projection from the primary by \\((a_{\\perp,2}, a_{\\perp,3})\\sim (3.5, 4.0)\\)~AU. The lens of KMT-2018-BLG-2119 is the first triple stellar system detected via microlensing.

Recently, there have been reports of various types of degeneracies in the interpretation of planetary signals induced by planetary caustics. In this work, we check whether such degeneracies persist in the case of well-covered signals by analyzing the lensing event KMT-2021-BLG-1150, for which the light curve exhibits a densely and continuously covered short-term anomaly. In order to identify degenerate solutions, we thoroughly investigate the parameter space by conducting dense grid searches for the lensing parameters. We then check the severity of the degeneracy among the identified solutions. We identify a pair of planetary solutions resulting from the well-known inner-outer degeneracy, and find that interpreting the anomaly is not subject to any degeneracy other than the inner-outer degeneracy. The measured parameters of the planet separation (normalized to the Einstein radius) and mass ratio between the lens components are \\((s, q)_{\\rm in}\\sim (1.297, 1.10\\times 10^{-3})\\) for the inner solution and \\((s, q)_{\\rm out}\\sim (1.242, 1.15\\times 10^{-3})\\) for the outer solution. According to a Bayesian estimation, the lens is a planetary system consisting of a planet with a mass \\(M_{\\rm p}=0.88^{+0.38}_{-0.36}~M_{\\rm J}\\) and its host with a mass \\(M_{\\rm h}=0.73^{+0.32}_{-0.30}~M_\\odot\\) lying toward the Galactic center at a distance \\(D_{\\rm L} =3.8^{+1.3}_{-1.2}\\)~kpc. By conducting analyses using mock data sets prepared to mimic those obtained with data gaps and under various observational cadences, it is found that gaps in data can result in various degenerate solutions, while the observational cadence does not pose a serious degeneracy problem as long as the anomaly feature can be delineated.

We inspect the microlensing data of the KMTNet survey collected during the 2018--2020 seasons in order to find lensing events produced by binaries with brown-dwarf companions. In order to pick out binary-lens events with candidate BD lens companions, we conduct systematic analyses of all anomalous lensing events observed during the seasons. By applying the selection criterion with mass ratio between the lens components of \\(0.03\\lesssim q\\lesssim 0.1\\), we identify four binary-lens events with candidate BD companions, including KMT-2018-BLG-0321, KMT-2018-BLG-0885, KMT-2019-BLG-0297, and KMT-2019-BLG-0335. For the individual events, we present the interpretations of the lens systems and measure the observables that can constrain the physical lens parameters. The masses of the lens companions estimated from the Bayesian analyses based on the measured observables indicate that the probabilities for the lens companions to be in the brown-dwarf mass regime are high: 59\\%, 68\\%, 66\\%, and 66\\% for the four events respectively.

The light curve of the microlensing event KMT-2021-BLG-0240 exhibits a short-lasting anomaly with complex features near the peak at the 0.1~mag level from a single-lens single-source model. We conducted modeling of the lensing light curve under various interpretations to reveal the nature of the anomaly. It is found that the anomaly cannot be explained with the usual model based on a binary-lens (2L1S) or a binary-source (1L2S) interpretation. However, a 2L1S model with a planet companion can describe part of the anomaly, suggesting that the anomaly may be deformed by a tertiary lens component or a close companion to the source. From the additional modeling, we find that all the features of the anomaly can be explained with either a triple-lens (3L1S) model or a binary-lens binary-source (2L2S) model obtained under the 3L1S interpretation. However, it is difficult to validate the 2L2S model because the light curve does not exhibit signatures induced by the source orbital motion and the ellipsoidal variations expected by the close separation between the source stars according to the model. We, therefore, conclude that the two interpretations cannot be distinguished with the available data, and either can be correct. According to the 3L1S solution, the lens is a planetary system with two sub-Jovian-mass planets in which the planets have masses of 0.32--0.47~\\(M_{\\rm J}\\) and 0.44--0.93~\\(M_{\\rm J}\\), and they orbit an M dwarf host. According to the 2L2S solution, on the other hand, the lens is a single planet system with a mass of \\(\\sim 0.21~M_{\\rm J}\\) orbiting a late K-dwarf host, and the source is a binary composed of a primary of a subgiant or a turnoff star and a secondary of a late G dwarf. The distance to the planetary system varies depending on the solution: \\(\\sim 7.0\\)~kpc according to the 3L1S solution and \\(\\sim 6.6\\)~kpc according to the 2L2S solution.

The light curve of the microlensing event KMT-2021-BLG-1898 exhibits a short-term central anomaly with double-bump features that cannot be explained by the usual binary-lens or binary-source interpretations. With the aim of interpreting the anomaly, we analyze the lensing light curve under various sophisticated models. We find that the anomaly is explained by a model, in which both the lens and source are binaries (2L2S model). For this interpretation, the lens is a planetary system with a planet/host mass ratio of \\(q\\sim 1.5\\times 10^{-3}\\), and the source is a binary composed of a turn off or a subgiant star and a mid K dwarf. The double-bump feature of the anomaly can also be depicted by a triple-lens model (3L1S model), in which the lens is a planetary system containing two planets. Among the two interpretations, the 2L2S model is favored over the 3L1S model not only because it yields a better fit to the data, by \\(\\Delta\\chi^2=[14.3\\)--18.5], but also the Einstein radii derived independently from the two stars of the binary source result in consistent values. According to the 2L2S interpretation, KMT-2021-BLG-1898 is the third planetary lensing event occurring on a binary stellar system, following MOA-2010-BLG-117 and KMT-2018-BLG-1743. Under the 2L2S interpretation, we identify two solutions resulting from the close-wide degeneracy in determining the planet-host separation. From a Bayesian analysis, we estimate that the planet has a mass of \\(\\sim 0.7\\)--0.8~\\(M_{\\rm J}\\), and it orbits an early M dwarf host with a mass of \\(\\sim 0.5~M_\\odot\\). The projected planet-host separation is \\(\\sim 1.9\\)~AU and \\(\\sim 3.0\\)~AU according to the close and wide solutions, respectively.